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On Ordinary Words of Standard Reed-Solomon Codes over Finite Fields

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Algebra Colloquium 2021年第4期28卷 569-580页

作者： Xiaofan Xu shaofang hong Mathematical College Sichuan UniversityChengdu 610064China Department of Mathematics Sichuan Tourism UniversityChengdu 610100China

Reed-Solomon codes are widely used to establish a reliable channel to transmit information in digital communication which has a strong error correction capability and a variety of efficient decoding *** we use the maximum likelihood decoding(MLD)algorithm in the decoding process of Reed-Solomon *** algorithm relies on determining the error distance of received word.Dür,Guruswami,Wan,Li,hong,Wu,Yue and Zhu et *** some results on the error *** the Reed-Solomon code C,the received word u is called an ordinary word of C if the error distance d(u,C)=n-deg u(x)with u(x)being the Lagrange interpolation polynomial of *** introduce a new method of studying the ordinary *** fact,we make use of the result obtained by *** and *** on the decomposition of certain polynomials over the finite field to determine all the ordinary words of the standard Reed-Solomon codes over the finite field of q *** completely answers an open problem raised by Li and Wan in[On the subset sum problem over finite fields,Finite Fields Appl.14(2008)911-929].

关键词： Reed-Solomon code ordinary word Lagrange interpolation polynomial finite field

A Note on the Tu-Deng Conjecture

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Journal of Systems Science & Complexity 2015年第3期28卷 702-724页

作者： CHENG Kaimin hong shaofang Zhong Yuanming Mathematical College Sichuan University Department of Mathematics Sichuan University Jinjiang College

Let k be a positive integer. For any positive integer x =∑i=0^∞xi2^i, where xi = 0, 1,we define the weight w（x） of x by w（x）：= ∑i=0^∞xi. For any integer t with 0 〈 t 〈 2^k- 1, let St ：= {（a,b）∈ Z^2｜a＋b≡t（mod 2^k-1）,w（a）＋w（b）〈k,0≤a,b≤2^k-2}.This paper gives explicit formulas for cardinality of St in the cases of w（t） ≤ 3 and an upper bound for cardinality of St when w（t） = 4. From this one then concludes that a conjecture proposed by Tu and Deng in 2011 is true if w（t） ≤ 4.

关键词： 2-adic valuation Tu-Deng conjecture weight.

On deep holes of standard Reed-Solomon codes

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Science China Mathematics 2012年第12期55卷 2447-2455页

作者： WU RongJun hong shaofang Mathematical College Sichuan University Chengdu 610064 China Yangtze Center of Mathematics Sichuan University Chengdu 610064 China

Determining deep holes is an important open problem in decoding Reed-Solomon codes. It is well known that the received word is trivially a deep hole if the degree of its Lagrange interpolation polynomial equals the dimension of the Reed-Solomon code. For the standard Reed-Solomon codes [p-1, k]p with p a prime, Cheng and Murray conjectured in 2007 that there is no other deep holes except the trivial ones. In this paper, we show that this conjecture is not true. In fact, we find a new class of deep holes for standard Reed-Solomon codes [q-1, k]q with q a power of the prime p. Let q≥4 and 2≤k≤q-2. We show that the received word u is a deep hole if its Lagrange interpolation polynomial is the sum of monomial of degree q-2 and a polynomial of degree at most k-1. So there are at least 2(q-1)qk deep holes if k q-3.

关键词： deep hole Reed-Solomon code cyclic code BCH code DFT IDFT

New Lower Bounds for the Least Common Multiples of Arithmetic Progressions

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Chinese Annals of Mathematics,Series B 2013年第6期34卷 861-864页

作者： Rongjun WU Qianrong TAN shaofang hong Mathematical College Sichuan University School of Mathematics and Computer Science Panzhihua University Yangtze Center of Mathematics Sichuan University

Abstract For relatively prime positive integers u0 and r, and for 0 〈 k ≤ n, define uk ：= u0 ＋ kr. Let Ln ：= 1cm（u0,u1,... ,un） and let a,l≥2 be any integers. In this paper, the authors show that, for integers α≥ a, r ≥max（a,l - 1） and n ≥lατ, the following inequality holds Ln≥u0r^（l-1）α＋a-l（r＋1）^***, letting l = 3 yields an improvement on the best previous lower bound on Ln obtained by hong and Kominers in 2010.

关键词： Arithmetic progression Least common multiple Lower bound

Additive characters and orthogonal systems of polynomials in several indeterminates over residue class rings

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Chinese Science Bulletin 1998年第4期43卷 275-277页

作者： hong shaofang Department of Mathematics, Sichuan University, Chengdu 610064, China Department of Matherrratics Sichuan University Chcngdu China

Let m, n and k be positive integers, m>1 and k≤n . Let Z m =Z/ m Z denote the residue class ring modulo m . Let Z denote the group of additive characters of ring Z m , x 0 denote the identity of Z . A necessary and sufficient condition for the system f\-1, ..., f\-k∈ Z m [ x\-1, ..., x\-n ] to be orthogonal is given: for all additive characters ψ 1, ..., ψ k ∈Z with ψ i≠x 0 for some i, 1≤i≤k, ∑(c\-1, ..., c\-n)∈ Z n m ψ(f\-1(c\-1, ..., c\-n))...ψ k(f\-k(c\-1, ..., c\-n))=0. As corollaries, the result of Shiue_Sun_Zhang and the result of Sun are obtained.

关键词： orthogonal system additive character permutation polynomial Jacobi matrix.

关于本原射影Reed-Solomon码的深洞

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中国科学：数学 2018年第8期48卷 1087-1094页

作者：徐小凡洪绍方许永超四川大学数学学院成都610064

本原射影Reed-Solomon码是数字通信领域中的一类重要的极大距离可分码.在本原射影ReedSolomon码的译码过程中,人们通常采用极大似然译码算法.对于一个收到的向量u∈F_q^n,极大似然译码算法关键在于确定向量u关于码C的错误距离d(u,C).熟... 详细信息

本原射影Reed-Solomon码是数字通信领域中的一类重要的极大距离可分码.在本原射影ReedSolomon码的译码过程中,人们通常采用极大似然译码算法.对于一个收到的向量u∈F_q^n,极大似然译码算法关键在于确定向量u关于码C的错误距离d(u,C).熟知d(u,C)≤ρ(C),其中ρ(C)为码C的覆盖半径.若d(u,C)=ρ(C),则称u为码C的深洞.本文得到了本原射影Reed-Solomon码PPRS_q(F_q~*,k)的一类深洞.实际上,利用有限域F_q上极大距离可分码的生成矩阵,本文证明如下结果成立:如果q≥4,整数k满足2≤k≤q-2,收到的向量u的前q-1个分量的Lagrange插值多项式为u(x)=λx^(q-2)+f≤k-2(x),其中λ∈F_q~*,f≤k-2(x)为F_q上次数不超过k-2的多项式,并且u的第q个分量为0,那么u是本原射影Reed-Solomon码PPRSq(F_q~*,k)的一个深洞.

关键词：本原射影Reed-Solomon码 MDS(maximum distance separable)码深洞

Automatic Monitoring Electronic Tongue with MEAs for Environmental Analysis

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稀有金属材料与工程 2006年第A03期35卷 381-384页

作者： shaofang Zou hong Men Yi Li Yinping Wang Ping Wang Biosensor National Special Laboratory Key Laboratory of Biomedical Engineering of Education Ministry Department of Biomedical Engineering Zhejiang University Hangzhou 310027 China State Key Laboratory of Transducer Technology Chinese Academy of Sciences Shanghai 200050 China

An automatic monitoring electronic tongue based on differential pulse stripping voltammetry (DPSV) was developed for heavy metals *** detections of trace Zn(Ⅱ),Cd(Ⅱ),Pb(Ⅱ),Cu(Ⅱ),Fe(Ⅲ) and Cr(Ⅲ) in water samples were performed with three electrochemical *** sensor chip combined a silicon-based Hg-coated Au microelectrode array (MEA) as the working electrode on one side with an Ag/AgCl reference electrode and a Pt counter electrode on the other *** a computer controlled multipotentiostat,pumps and valves,the electronic tongue realized in-situ real-time detection of the six metals mentioned above at parts-per-billion level without manual operation.

关键词： electronic tongue heavy metals automatic monitoring microelectrode array multipotentiostat

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一种新型汞离子选择薄膜传感器

分析化学 2005年第3期33卷 428-431页

作者：门洪,邹绍芳,Andrey Legin,王平生物医学工程教育部重点实验室杭州310027 杭州310027 杭州310027 浙江大学生物医学工程与仪器科学学院生物传感器国家专业实验室生物医学工程教育部重点实验室浙江大学生物医学工程与仪器科学学院生物传感器国家专业实验室生物医学工程教育部重点实验室 Chemistry Department.St.Petersburg University St.Petersburg 199034 Russia 浙江大学生物医学工程与仪器科学学院生物传感器国家专业实验室

采用脉冲激光沉积技术,在光寻址电位传感器表面上沉积了对二价汞离子敏感的薄膜,制备了一种新型汞离子选择薄膜传感器,靶材成分为HgAgIS,基底为p型单晶硅片,金属接触层为Cr/Au。该薄膜传感器在3星期内显示了良好的重复性和稳定性;检出限... 详细信息

采用脉冲激光沉积技术,在光寻址电位传感器表面上沉积了对二价汞离子敏感的薄膜,制备了一种新型汞离子选择薄膜传感器,靶材成分为HgAgIS,基底为p型单晶硅片,金属接触层为Cr/Au。该薄膜传感器在3星期内显示了良好的重复性和稳定性;检出限为3×10-6mol/L;响应时间小于2min,适用pH范围小于2。对干扰离子和迟滞效应等也进行了研究。该传感器具有测量快速灵活、所需样品少、动态范围宽等特点,因为把电位信号转化为对光激发的交流电流信号进行测量,所以提高了灵敏度。同时也证明了脉冲激光沉积是适合制备薄膜传感器的一种新技术。

关键词：薄膜传感器光寻址电位传感器脉冲激光沉积汞离子敏感

The chemical reprogramming of unipotent adult germ cells towards authentic pluripotency and de novo establishment of imprinting

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Protein & Cell 2023年第7期14卷 479-498页

作者： Yuhan Chen Jiansen Lu Yanwen Xu Yaping Huang Dazhuang Wang Peiling Liang shaofang Ren Xuesong Hu Yewen Qin Wei Ke Ralf Jauch Andrew Paul Hutchins Mei Wang Fuchou Tang Xiao-Yang Zhao State Key Laboratory of Organ Failure Research Department of Developmental BiologySchool of Basic Medical SciencesSouthem Medical UniversityGuangzhou 510515China Beijing Advanced Innovation Center for Genomics School of Life SciencesPeking UniversityBeijing 100871China Biomedical Pioneering Innovation Center Ministry of Education Key Laboratory of Cell Proliferation and DifferentiationBeijing 100871China Departmentof Urology Nanfang HospitalSouthem Medical UniversityGuangzhou 510515China School of Biomedical Sciences Li Ka Shing Faculty of MedicineThe University of Hong KongHong Kong SARChina Department of Biology Southerm University of Science and TechnologyShenzhen 518055China Department of Neonatology Zhujiang HospitalSouthem Medical UniversityGuangzhou 510280China Guangdong Provincial Key Laboratory of Construction and Detection in Tissue Engineering Southem Medical UniversityGuangzhou 510515China Department of Gynecology Zhujiang HospitalSouthern Medical UniversityGuangzhou 510280China Key Laboratory of Mental Health of the Ministry of Education Guangzhou 510515China Bioland Laboratory(Guangzhou Regenerative Medicine and Health Guangdong Laboratory) Guangzhou 510005China Department of Plastic Surgery Affliated Hangzhou First People's HospitalZhejiang University School of MedicineHangzhou 310006China

Although somatic cells can be reprogrammed to pluripotent stem cells(PsCs)with pure chemicals,authentic pluripotency of chemically induced pluripotent stem celis(CipsCs)has never been achieved through tetraploid complementation *** reprogramming of spermatogonial stem cells(ssCs)was another non-transgenic way to obtain PsCs,but this process lacks mechanistic ***,we reconstructed the trajectory of mouse SsC reprogramming and developed a five-chemical combination,boosting the reprogramming effciency by nearly 80-to *** importantly,chemical induced germline-derived PsCs(5C-gPSCs),but not gpsCs and chemical induced pluripotent stem cells,had authentic pluripotency,as determined by tetraploid ***,ssCs traversed through an inverted pathway of in vivo germ ceil development,exhibiting the expression signatures and DNA methylation dynamics from spermatogonia to primordial germ cells and further to ***,ssC-specific imprinting control regions switched from biallelic methylated states to monoallelic methylated states by imprinting demethylation and then re-methylation on one of the two alleles in 5c-gPsCs,which was apparently distinct with the imprinting reprogramming in vivo as DNA methylation simultaneously occurred on both *** work sheds ight on the unique regulatory network underpinning SsC reprogramming,providing insights to understand generic mechanisms for cell-fate decision and epigenetic-relateddisorders in regenerative medicine.

关键词： reprogramming spermatogonial stem cell tetraploid complementation imprinting